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Unformatted text preview: PHYS 3202 Classical Mechanics II - Homework #8 Due at 12:05pm, Friday April 8, 2011 in the class Please show intermediate steps of your calculations. Problem 1 (10 points): Calculate the inertia tensor of a system of four point- like objects with mass m each, connected by rigid massless rods to form a regular tetrahedron ( http://en.wikipedia.org/wiki/Tetrahedron ). The length of each edge is a . The total mass of the system is 4 m . The coordinates of the four masses can be given as (+ a 3 , ,- a 2 6 ); (- a 2 3 , + a 2 ,- a 2 6 ); (- a 2 3 ,- a 2 ,- a 2 6 ); (0 , , + r 3 8 a ) . You may give calculation details for one diagonal element and one off-diagonal ele- ment of the inertia tensor, and simply list final answers for all remaining 7 elements. Problem 2 (10 points): Which of the following matrices can NOT represent an inertia tensor? Give your reasoning for each. c is a positive constant....
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